I meant to say that, indeed, there must be some concept of CPU for a memory address to have a meaning, and for this concept of CPU to be as widely applicable as possible, surely defining it as abstract as possible is the way to go. Ergo, the idea of a C abstract machine.

Anyway, other people in this thread are discussing the matter more accurately and in more details than I could hope to do, so I'll leave it like that.

I am in no way trying to judge you; rather, I'm trying to get closer to the truth in that matter, and your input is valuable, as it points out a discrepancy wrt TFA, but it is also subject to caution, since it reports the results of only one chess player (right?). Furthermore, both in the case of TFA and this youtuber, we don't have full access to their whole experiments, so we can't reproduce the results, nor can we try to understand why there is a difference.

I might very well be mistaken though, and I am open to criticisms and corrections, of course.

If I were to take that sentence literally, I would ask for at least 199 other examples, but I imagine that it was just a figure of speech. Nevertheless, if that's only one player complaining (even several times), can we really conclude that ChatGPT cannot play? Is that enough evidence, or is there something else at work?

I suppose indeed one could, if one expected an LLM to be ready to play out of the box, and that would be a fair criticism.

> Machines are good at applying rules, so when they fail to apply rules correctly, it means they have incorrect, incomplete, or totally absent models.

If this line of reasoning applies to machines, but LLMs aren't machines, how can you derive any of these claims?

"A implies B" may be right, but you must first demonstrate A before reaching conclusion B..

> I think we are discussing whether LLMs can emulate chess playing machines

That is incorrect. We're discussing whether LLMs can play chess. Unless you think that human players also emulate chess playing machines?

> For one, gpt-3.5-turbo-instruct rarely suggests illegal moves, even in the late game. This requires “understanding” chess. If this doesn’t convince you, I encourage you to write a program that can take strings like 1. e4 d5 2. exd5 Qxd5 3. Nc3 and then say if the last move was legal.

However, I can't say if LLMs fall in the "statistical AI" category.

Do you have any evidence of that? TFA doesn't talk about the nature of these errors.

That's assuming that, somehow, a LLM is a machine. Why would you think that?

But this math analogy is not quite appropriate: there's abstract math and arithmetic. A good math practitioner (LLM or human) can be bad at arithmetic, yet good at abstract reasoning. The later doesn't (necessarily) requires the former.

In chess, I don't think that you can build a good strategy if it relies on illegal moves, because tactics and strategies are tied.

However, in this specific instance, even if the text cannot be changed, couldn't the error itself in the server be processed and signaled differently, eg. by returning a Status Code 413[1], since clients ought to recognize that status code anyway?

[1]: https://developer.mozilla.org/en-US/docs/Web/HTTP/Status/413

What did you try? What were the research directions at the time?

When I first read the article, the sequence of subgroups that were described evoked that image of a combination lock to me:

< UR >

< U, R >

< U, R, D >

< U, R, D, L >

< U, R, D, L, F >

The behavior of the basic operations on the cube reminds me of the product of quaternion base vectors (i,j,k). For instance, the product of i and j would yield either k or -k depending on the order of i and j. I think the point I wanted to make is that on a combination lock, each operation on a wheel only affect that wheel, not the others, so one cannot produce another operation by combining several of them, like what we see with quaternions. However, on the cube, it is often possible to go from one combination to another by different sequences of different operations.

But that may not matter much, if all we care about is going through every possible combination exactly once, just like what one does when using gray code on binary numbers (which is why I alluded to that in my other post), and that for that purpose we can find a set of sequences of operations - let's call them large operations - that are orthogonal (and thus emulating the rotating wheel aspect of the combination lock). I suppose that these subgroups represent the large operations. The problem you bring up now is that these large operations are not commutative, and so finding a correct way to apply them to build the circuit is more involved than simply spinning the wheels on a lock.

Is that correct?

Edit: I just had a first look at cayley graphs on wikipedia, and they use quaternion rotations as an example!

Isn't that the rule that Uber itself already imposes on its customers and drivers?